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Constructibility and Mathematical Existence

Charles S. Chihara

Published in print:
1991
Published Online:
November 2003
ISBN:
9780198239758
eISBN:
9780191597190
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0198239750.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

A continuation of the study of mathematical existence begun in Ontology and the Vicious‐Circle Principle (published in 1973); in the present work, Quine's indispensability argument is rebutted by the ... More


Mathematical Structuralism

Charles S. Chihara

in Constructibility and Mathematical Existence

Published in print:
1991
Published Online:
November 2003
ISBN:
9780198239758
eISBN:
9780191597190
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198239750.003.0007
Subject:
Philosophy, Logic/Philosophy of Mathematics

The first of six chapters in which rival views are critically evaluated and compared with the Constructibility view described in earlier chapters. The views considered here (forms of ‘Structuralism’) ... More


Recent Attempts at Blunting the Indispensability Thesis

Michael D. Resnik

in Mathematics as a Science of Patterns

Published in print:
1999
Published Online:
November 2003
ISBN:
9780198250142
eISBN:
9780191598296
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198250142.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

The indispensability thesis maintains both that using mathematical terms and assertions is an indispensable part of scientific practice and that this practice commits science to mathematical objects ... More


Grounding in Mathematical Structuralism

John Wigglesworth

in Reality and its Structure: Essays in Fundamentality

Published in print:
2018
Published Online:
June 2018
ISBN:
9780198755630
eISBN:
9780191816772
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198755630.003.0012
Subject:
Philosophy, Metaphysics/Epistemology

The grounding relation is thought to have certain structural properties: irreflexivity, asymmetry, transitivity, and well-foundedness. This paper examines a putative case of grounding that serves as ... More


Categories for the Working Philosopher

Elaine Landry (ed.)

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198748991
eISBN:
9780191811593
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198748991.001.0001
Subject:
Philosophy, History of Philosophy

Borrowing from the title of Saunders Mac Lane’s seminal work Categories for the Working Mathematician, this book aims to bring the concepts of category theory to philosophers working in areas ranging ... More


Bicollective Ground: Towards a (Hyper)Graphic Account

Jon Erling Litland

in Reality and its Structure: Essays in Fundamentality

Published in print:
2018
Published Online:
June 2018
ISBN:
9780198755630
eISBN:
9780191816772
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198755630.003.0008
Subject:
Philosophy, Metaphysics/Epistemology

Grounding is bicollective if it is possible for some truths δ‎0, δ‎1, … to be grounded in the some truths γ‎0, γ‎1, …. without its being the case that each δ‎i is grounded in some subcollection of ... More


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